The ongoing development of digital modeling software allows design to significantly depart from the Euclidean geometrical limits that paralleled architectural thinking for many centuries. Before digital technologies, curved surfaces and forms were the product of approximations using tangents to circular arcs and straight-line segments that were translated from drawings to the building site. In freeing the designer from the constraints of Cartesian space, digital modeling programs typically use the topological geometry of continuous curves and surfaces. Also known as “rubber sheet” geometry, topological geometry enables curvilinear surfaces to be described as NURBS. The curves and surfaces produced by NURBS provide a high degree of formal control via “control points,” “weights,” and “knots.” Extending the rubbersheet analogy, it is easy to imagine how if we fixed certain points of it, added weights to others, and affected it from other positions we would be able to see the resultant deformations as we varied our actions. NURBS provide the mathematical underpinning for this very simplified description of the process, and allow the user to develop complex geometrical designs computationally and transfer this data using CNC machinery.
The key advantage of NURBS is their role in the production of a wide range of geometric forms, ranging from simple volumetric solids to extensively detailed, complex surfaces. In addition, NURBS offer a very efficient way of representing data by using comparatively few steps for shape computation, which is why many digital modeling software packages use them. If this all sounds rather abstract, then it may help to think about them as Branko Kolarevic suggests: “NURBS are a digital equivalent of the drafting splines used to draw the complex curves in the cross-sections of ship hulls and airplane fuselages. Those splines were flexible strips made of plastic, wood or metal that would be bent to achieve a desired smooth curve, with weights attached to them in order to maintain the given shape.”9
The “rubber sheet” geometry afforded by NURBS has been instrumental in the design and production of many contemporary architectural projects. While such design tools may allow the fabrication of curvilinear forms this is not always the case, as shown in these design-development screenshots for ONL’s iWeb project in which the NURBS are used to generate specific planar components in relation to each other. (Compare these images with the final design on page 13.)
UNStudio’s floating and multidirectional space for the Burnham Pavilion in Chicago is a direct result of its curvilinear geometry, developed using NURBS to inform the design and fabrication data.
In designing a summer pavilion for the German Architecture Museum in Frankfurt am Main, Barkow Leibinger developed a series of unique radial tubes with radii that produce a circular, arched space. The initial concept stemmed from a “slinky” toy that was explored through physical models and digital 3-D modeling to refine and analyze its design variables and performance. The full-size prototype was clad with a series of polycarbonate shingles, the arrangement and shapes of which were determined by computer scripting to optimize each component within the overall system.
The Maison Folie, Lille Wazemmes, designed by NOX provides an undulating stainless-steel skin that responds to artificial light, providing dramatic effects at night.
In daytime, the scheme’s form has a more solid appearance that retains its curvilinear properties but seeks to respond to the historic urban fabric of its context.
NURBS can be made using a range of software programs. In this example, curves have been drawn in CAD and manipulated using their control points (left). A NURB surface is generated from the control-point curves using a “loft” command (right).
In West 8’s design for the Puentes Cascara Bridge, a key element of their masterplan in Madrid, the intention was to make an infrastructural element that connected to the adjacent park in terms of scale. The design was conceived as a concrete dome, from which the bridge was hung. The bridge form was explored using drawings and rapid-prototyped models to enable further refinement of the shell geometry prior to construction.
The completed scheme demonstrates the smooth geometry of the concrete, which, when coupled with the slim steel deck and fine cable suspension, produces a sculptural piece in keeping with the original concept.
